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In this article, we discuss a new coupled system of fractional differential equations with integral boundary conditions $$textstylebegin{cases} D^{alpha}u(t)+f(t,v(t))=a,quad 0u003c tu003c 1, D^{beta}v(t)+g(t,u(t))=b,quad 0u003c tu003c 1, u(0)=0,qquad u(1)=int_{0}^{1} phi(t)u(t),dt, v(0)=0,qquad v(1)=int_{0}^{1} psi(t)v(t),dt, end{cases} $$where (1u003c alpha,betale2, f,g in C([0,1]times(-infty,+infty ),(-infty,+infty)), phi,psiin L^{1}[0,1]), (a,b) are constants and D denotes the usual Riemann-Liouville fractional derivative. Based upon a fixed point theorem of increasing φ-((h,e))-concave operators, we establish the existence and uniqueness of solutions for the new coupled system dependent on two constants. And then the obtained result is well demonstrated with the aid of an interesting example.

Unique solutions for a new coupled system of fractional differential equations